1. Field of the Invention
The present invention relates to a viterbi detector for use in a disk storage system which uses an RLL(Run-Length Limited) coding and an NRZ1 (Non-Return to Zero 1) recording method and applies a (1+D) PR channel.
2. Discussion of Related Art
Generally, in a lower density data storage system, there scarcely occurs an Inter-Symbol Interference (ISI) and thus there is no need to equalize the waveform when detecting an original signal from a decoder.
However, with the development of high density storage systems which store more information in a limited area, we cannot overlook inter-symbol interference. Many techniques have been proposed to solve this problem and one of these techniques is a Partial Response Maximum Likelihood (PRML) using a viterbi detector.
Ferguson has proposed a method for simply embodying the viterbi detector in the case that the inter-symbol interference occurs in the (1.+-.D) channel, and description will be made herein on the case of the (1+D).
FIG. 1 is a trellis diagram showing a detector having two states. It shows the possibility of passing a branch for X.sub.k.sup.++, X.sub.k.sup.+-, X.sub.k.sup.-+ and the input .gamma..sub.k of the viterbi detector, and this is referred to as a branch matrix. In the figure, .sup.++, .sup.+-, .sup.-+, .sup.-- show that from what state to what state the branch is changed. In addition, .lambda..sub.k.sup.+ or .lambda..sub.k.sup.- is the value obtained by adding all branch matrixes while being passed to the node, and is referred to as a path matrix.
In a general viterbi detector, the path matrix is determined as follows: EQU .lambda..sub.k+1.sup.- =mim(.lambda..sub.k.sup.- +x.sub.k.sup.--, .lambda..sub.k.sup.+ +x.sub.k.sup.+-) EQU .lambda..sub.k+1.sup.+ =mim(.lambda..sub.k.sup.- +X.sub.k.sup.-+, .lambda..sub.k.sup.+ +X.sub.k.sup.++) equation (1)
If .DELTA..sub.k .congruent..lambda..sub.k.sup.- -.lambda..sub.k.sup.+, Q.sub.k+1.sup.- .congruent..lambda..sub.k+1.sup.- -.lambda..sub.k.sup.+, Q.sub.k+1.sup.- .congruent..lambda..sub.k+1.sup.+ .congruent..lambda..sub.k+1.sup.- .lambda..sub.k are applied to the equation (1), EQU Q.sub.k+1.sup.- =mim(.DELTA..sub.k +X.sub.k.sup.--, X.sub.k.sup.+-) EQU Q.sub.k+1.sup.+ =mim(.DELTA..sub.k +X.sub.k.sup.-+, X.sub.k.sup.++)equation (2) EQU Q.sub.k+1.sup.- -Q.sub.k+1.sup.+ =(.lambda..sub.k+1 -.lambda..sub.k.sup.-)-(.lambda..sub.k+1 -.lambda..sub.k.sup.+)=.DELTA..sub.k+1
That is, in the trellis diagram, two branches are met at one node. In this algorithm, the previous path matrix is added to each of two branch matrixes and then the path with the smaller value is selected as a new path.
FIG. 2 is a trellis diagram in the case of (1+D), and the branch matrix values are defined as follows: EQU X.sub.k.sup.++ =(.gamma..sub.k -2A).sup.2, X.sub.k.sup.+- =X.sub.k.sup.-+ =.gamma..sub.k.sup.2, X.sub.k.sup.-- =(.gamma..sub.k -2A).sup.2.
Thus, the above equation (2) becomes
Q.sub.k+1.sup.- =mim(.DELTA..sub.k +(.gamma..sub.k -2A).sup.2, .gamma..sub.k.sup.2) EQU Q.sub.k+1.sup.+ =mim(.DELTA..sub.k +.gamma..sub.k.sup.2, (.gamma..sub.k -2A).sup.2) equation (3).
FIGS. 3A to 3D show all possible cases of FIG. 1, and each case can be analyzed with the above equation (3) and FIG. 2 as follows.
Firstly, a negative merging as shown in FIG. 3A can be analyzed as follows: EQU (S.sup.- .fwdarw.S.sup.-): .DELTA..sub.k +(.gamma..sub.k +2A).sup.2 &lt;.gamma..sub.k.sup.2 .fwdarw..DELTA..sub.k /4A&lt;-.gamma..sub.k -A EQU (S.sup.- .fwdarw.S.sup.+): .DELTA..sub.k +.gamma..sub.k.sup.2 &lt;(.gamma..sub.k +2A).sup.2 .fwdarw..DELTA..sub.k /4A&lt;-.gamma..sub.k +A EQU .thrfore..DELTA..sub.k /4A&lt;-.gamma..sub.k -A (.BECAUSE.A&gt;0) EQU .DELTA..sub.k+1 /4A={.DELTA..sub.k +(.gamma..sub.k +2A).sup.2 -(.DELTA..sub.k +.gamma..sub.k.sup.2)}/4A=.gamma..sub.k +Aequation (4)
Secondly, a cross over as shown in FIG. 3B can be analyzed as follows: EQU (S.sup.- .fwdarw.S.sup.-): .DELTA..sub.k +(.gamma..sub.k +2A).sup.2 &gt;.gamma..sub.k.sup.2 .fwdarw..DELTA..sub.k /4A&gt;-.gamma..sub.k -A EQU (S.sup.- .fwdarw.S.sup.+): .DELTA..sub.k +.gamma..sub.k.sup.2 &lt;(.gamma..sub.k +2A).sup.2 .fwdarw..DELTA..sub.k /4A&lt;-.gamma..sub.k +A EQU .thrfore.-.gamma..sub.k -A&lt;.gamma..sub.k /4A&lt;-.gamma..sub.k +A EQU .DELTA..sub.k+1 /4A={.gamma..sub.k.sup.2 -(.DELTA..sub.k +.gamma..sub.k.sup.2)}/4A=-.DELTA..sub.k /4A equation (5)
Thirdly, a positive merging as shown in FIG. 3C can be analyzed as follows: EQU (S.sup.- .fwdarw.S.sup.-): .DELTA..sub.k +(.gamma..sub.k +2A).sup.2 &gt;.gamma..sub.k.sup.2 .fwdarw..DELTA..sub.k /4A&gt;-.gamma..sub.k -A EQU (S.sup.+ .fwdarw.S.sup.+): .DELTA..sub.k +.gamma..sub.k.sup.2 &gt;(.gamma..sub.k +2A).sup.2 .fwdarw..DELTA..sub.k /4A&gt;-.gamma..sub.k +A EQU .thrfore.-.gamma..sub.k /4A&gt;-.gamma..sub.k +A EQU .DELTA..sub.k+1 /4A=.gamma..sub.k -A equation (6)
Fourthly, no merging as shown in FIG. 3D can be analyzed as follows: EQU (S.sup.- .fwdarw.S.sup.-): .DELTA..sub.k +4A&lt;-.gamma..sub.k -A EQU (S.sup.+ .fwdarw.S.sup.+): .DELTA..sub.k /4A&gt;-.gamma..sub.k +A
There is no satisfied region . . . equation (7)
If defining that .DELTA..sub.k '=.DELTA..sub.k /4A, the results as shown in FIG. 4 can be obtained and FIG. 5 shows a general viterbi detector embodying the results.
However, in a conventional viterbi detector as described above, the decoded value can be obtained after lapse of a predetermined time, the performance depends on the value A and it is difficult to detect the value A.